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math.NA2025
High order regularization of nearly singular surface integrals
J. Thomas Beale, Svetlana Tlupova
Solutions of partial differential equations can often be written as surface integrals having a kernel related to a singular fundamental solution. Special methods are needed to eval…
math.NA2023
The adjoint double layer potential on smooth surfaces in and the Neumann problem
J. Thomas Beale, Michael Storm, Svetlana Tlupova
We present a simple yet accurate method to compute the adjoint double layer potential, which is used to solve the Neumann boundary value problem for Laplace's equation in three dim…
math.NA2023
Extrapolated regularization of nearly singular integrals on surfaces
J. Thomas Beale, Svetlana Tlupova
We present a method for computing nearly singular integrals that occur when single or double layer surface integrals, for harmonic potentials or Stokes flow, are evaluated at point…